I worked at Oak Ridge National Laboratory (ORNL) in the magnetic fusion program as a theoretical physicist for 25 years. I was responsible for much of the theory of neutral beam injection, a definitive study of orbits in tokamaks, and the magnetic design of stellarators. I was also involved in the engineering design issues of the ORNL stellarator ATF. I feel it is time to speak out on the direction of the world magnetic fusion (MF) program. The views expressed here are my own.

There are two serious contenders for MF devices: tokamaks and stellarators. Let me discuss a bit of the history behind these two approaches, because it sheds some light on the course of the world fusion program. 

Commonalities between tokamak and stellarator configurations

Both stellarators and tokamaks are doughnut-shaped tori that require a magnetic field line configuration in which the field lines wrap around the torus both the long way (toroidally) and the short way (poloidally). Thus the field lines wrap helically around the torus. The ratio of the number of transits a field line makes going toroidally to poloidally (once around the torus) is called the rotational transform. MF is based upon the fact that the charged particles (ions and electrons) that make up a plasma try to follow magnetic field lines. If their velocity does not align with the direction of the magnetic field (the field line), they also spiral around the field line. The radius of this spiral is called the gyroradius. Both tokamaks and stellarators rely upon closed field lines to contain a plasma. But because the field lines are not straight in a torus, the particles also drift vertically across the field lines. The rotational transform brings each field line to the top of the torus and to the bottom of the torus, so that this vertical drift cancels out. It is also critical that if one follows a magnetic field line around and around the torus, it should lie on a toroidal surface as opposed to filling a volume. (In a stellarator, this surface may be twisty and bumpy.) This surface is called a flux surface, and plasma properties (temperature, density, impurity content,...) are approximately constant on a flux surface.

Symmetry of the configuration is an important issue in plasma confinement. From a physics point of view. if there is a direction of symmetry in the magnetic configuration, it implies that there is an extra constant (of the charged particle's) motion. Because in the absence of collisions, the energy and the magnetic moment (the amount of magnetic field inside the gyrocircle) are also conserved, you can easily prove that the charged particle orbits will be contained forever in the configuration. Clearly this is an important consideration for good plasma confinement. 

The major physics differences between tokamaks and stellarators are in how the rotational transform is generated, and what happens to symmetry.

Tokamaks

If you remember the right-hand rule from your high school physics days, you can see that a simple configuration that would make a helical magnetic field around a torus would be a vertical wire (makes toroidal field lines) enclosed by a horizontal circular wire (makes poloidal field lines). If the vertical wire is in the center of the circular wire, there is clearly rotational symmetry. 

The Soviets recognized that the circular wire could be replaced by the plasma (which is a very good conductor) if they could induce toroidal current in it. They achieved this by making the plasma the secondary of a transformer, with the primary being a set of stacked circular coils in the center of the torus. They also replaced the central vertical wire with coils that go poloidally around the torus, which confines the toroidal field to the plasma volume. Finally, they added two circular coils above and below, and just outside the torus in distance from the symmetry axis (the major radius). These coils create a vertical magnetic field and allow experimenters the ability to change the major radius of the plasma.

Tokamak coil configuration
Tokamak coil configuration without vertical field coils. In reality, the blue helical field lines go s several times toroidally for each time they go around poloidally, the opposite of the situation depicted here, but it is harder to draw.
From http://www-fusion-magnetique.cea.fr/gb/fusion/physique/configtokamak.htm

There are several issues with the basic tokamak configuration. If there are a finite number of toroidal field (TF) coils (in red), the configuration is no longer truly axisymmetric. More TF coils reduce the ripple, but also cost more and reduce access to the plasma between the coils. The other problems lie with the plasma current itself.

There is no such thing as a DC transformer. The induced plasma current is caused by changing the current in the central (green) primary winding. The induced current is proportional the the time rate of change of the solenoid current. The solenoid usually starts at some maximum negative value and swings to some maximum positive value (or vice versa). After that, the shot is over unless the current can be sustained by some other means (current drive).

Another problem with plasma current is that it stores a huge amount of energy (400 megajoules in ITER—equivalent to a WW2 500-pound bomb) that can suddenly be released in what is called a major disruption. The largest tokamak in the world, the Joint European Torus (JET) in Culham England had such a disruption and rose up in the air and dented the vacuum vessel. These disruptions must be avoided at all costs. This is done by tailoring the profile of the current, which thus affects the rotational transform profile. It is not easy to measure the current profile, let alone to control it on a timescale short enough to avoid disruptions. A large amount of expensive equipment (not shown in the above diagram) is required to drive the current in the desired profile, and to modify the density and impurity profiles by injecting in frozen pellets of hydrogen or neon ice. In addition extra (non-symmetric) coils are employed to control plasma magnetohydrodynamic (MHD) instabilities.

Because of the plasma current, and the time-varying fields needed to induce it, large forces are exerted on all the magnets in the system. Everything must be designed to withstand these forces in both normal and abnormal (e.g., a coil fails) conditions. This requires more support structure, which raises costs and reduces access to the plasma.

I hope that the reader is getting the impression that I m not a fan of plasma current. Fortunately there is an alternative. 

Stellarators

The stellarator was invented before the tokamak by Lyman Spitzer of Princeton University (supposedly while riding a ski lift). Spitzer realized that you could create rotational transform by using more complicated helical coils. However before the days of computers most of these early stellarator devices had no flux surfaces, and were thus doomed to failure. The Soviets were also instrumental in creating the first successful stellarators, which had helical coils wrapped about a toroidal vacuum chamber in addition to toroidal field coils like on a tokamak. There is no plasma current, and the pulse length is only limited by how long you can keep supplying the current to the coils. 

Heliotron-J
Coil configuration of a "classical" stellarator. 

There are many varieties of stellarator with different names (e.g., heliotron, torsatron, etc) but they all have rotational transform generated by external coils, and they all have a nonaxisymmetric plasma. If all the coils are superconducting, and if the plasma can be heated continuously (e.g., by microwaves), a stellarator can be truly a steady-state device. There is no plasma current (or a very small one caused by the heated plasma itself), and hence no major disruptions. The huge forces on the tokamak coils due to the time-varying currents are eliminated. Nowadays, computer calculations ensure that stellarator designs have closed flux surfaces, however, toroidal symmetry is destroyed (see the pink plasma surface in the above image). This asymmetry led to enhanced so-called "ripple" transport across the flux surfaces. 

The largest operational stellarator, the Large Helical Device (LHD) in Toki, Japan is a superconducting machine capable of pulse lengths greater than a minute. Although it is a "classical" stellarator, it nonetheless performs just as well as a tokamak of a similar size.  When charged particles leave the device due to the ripple transport, a radial electric field arises, which seems to stop further loss.

However, Allen Boozer (Columbia University) looked hard at the equations of motion and discovered that in the absence of a plasma current, the particle orbits only depend on the magnitude of the magnetic field, B, rather than its directional field (B). In this case, he showed that the magnetic field can be derived from a scalar potential that obeys Laplace's Equation. Without going into technical details, this implies that you can create any periodic twisty toroidal surface (with some symmetry constraints), and it can be the outer flux surface of a stellarator plasma. This is quite an amazing observation because it decouples the physics of the stellarator plasma from the coil design. Boozer went further and asked "why can't you create a stellarator configuration that has a symmetric B, but an asymmetric B?" It turns out that you can (approximately) do this by using a computer to optimize the shape of the outer flux surface while calculating the symmetry of B. These are called quasitoroidal, quasihelical, and quasipoloidal configurations depending on the symmetry direction. These quasi configurations overcome the ripple transport problems of classical stellarators. A good summary of this process is given in a paper by Don Spong.

The second part of modern stellarator design is to create magnetic coils that will create the desired outer flux surface (OFS). The German group at IPP Garching discovered that you can enclose the desired outer flux surface with another (twisty) toroidal surface, and create a surface current distribution that creates the OFS. This surface current distribution can then be cut up into  physical coils that then create the entire stellarator field configuration.

W7-X with coils
The Wendelstein 7-X coil set and outermost flux surface. The colors correspond to the strength of B going from high (red) to low (blue)

The above image shows the Wendelstein 7-X (W7-X) stellarator, soon to be completed in Greifswald, Germany. The coils are unlinked, but are twisty, and the whole coil set is repeated 5 times going around the torus (5 field periods). W7-X is superconducting, and is the first large stellarator to be designed and built using the modern stellarator design principles. In a stellarator, coil accuracy is vital (a few mm) and these coils must be wound with a computer-controlled process. But each coil is much smaller than the ITER tokamak coils.

Even the modern stellarator (MS) is not without its configurational problems. There are two in particular that must be dealt with. The magnetic configuration of a MS is created by the fringing field of the coils. The closer the coils are to the plasma, the less twisty they need to be (twistier coils are harder to build and have higher forces). In a reactor, the space between the plasma and the coil needs to be at least a meter to allow room for the blanket and the shield. So, the size of a W7-X reactor (with the same coil set) is obtained by photographically enlarging the above image until the distance is about a meter. Because of the large hole in the center of the stellarator (higher aspect ratio), it also leads to a larger machine. The size limit on a reactor is determined by how much of a pulse on the electrical grid can be tolerated if a power plant drops offline. So there is a premium to finding designs with lower aspect ratio, and larger plasma-coil spacing to reduce the gigawatt electric output of the plant below about 3. There are advantages to the hole in the center of a stellarator. Holes are free, and they can be used to install heating and diagnostics on the high-B region of the device. They also make device assembly easier. 

Another advantage of stellarators is that there is an infinite variety of them. They can be designed to optimize different things. Tokamaks have just a few design parameters: The aspect ratio, magnetic field strength, toroidal current, and cross-sectional shape. Furthermore, the world stellarator community meets regularly to coordinate efforts. I edit the international newsletter Stellarator News. If you want to know the latest goings on in the stellarator community, drop me an e-mail and I can put you on the distribution list.

Assembling 2 modules of W7-X
Assembling two modules of W7-X. You can see the vacuum vessel inside one of the twisty coils. The cryostat (to keep the superconducting coils cool) is on the outside.

 

Why we should stop ITER

As pointed out in a good article in the New Yorker, ITER is a collaboration among many countries, and the management structure that entails is a recipe for delay, increased costs, and intransigence. For example, the engineering specifications for ITER call for a welded vacuum vessel, but an EU manufacturer decided to use a joint, and that decision could not be vetoed.

ITER
The ITER device. 

 

Engineering ITER is more difficult that engineering a stellarator of the same size for many reasons:

  • Systems must be built for driving, maintaining, and measuring the current profile, and they must be able to modify the profile in much less than a skin time (~1 s). Stellarator have no such systems.
  • The time-varying fields caused by the primary winding, and any possible plasma current disruption create huge forces and torques that require massive support structures. Stellarators have static magnetic fields, and thus a smaller support structure tailored for these specific fields.
  • The tokamak core is tightly packed. If something happens to the central solenoid, it will be difficult to replace. A stellarator has a hole in the center, and it is assembled in modules, which can be swapped out if needed.
  • ITER has normal coils (not shown) inside the vacuum vessel to control disruptions. They are cooled, and will be impossible to fix or replace if anything happens to them, or if they spring a leak. Stellarators need no disruption coils.
  • ITER requires neutral beams, electron cyclotron heating (ECH) and ion cyclotron heating (ICRH) just to drive the plasma current. In a stellarator, these systems can all be optimized and used just for heating the plasma.
  • Although a system of the scope of ITER (stellarator or tokamak) will have a finite-length shot, ITER is pulsed in principle, and a stellarator is not. In a reactor, this is a huge difference. The burning plasma core is hotter than the sun, the outside of the cryostat is at room temperature, and the inside should be just a few degrees K to keep the superconducting coils happy. This means that there is a tremendous temperature gradient in the region between the plasma and the coils. Materials that can take this thermal gradient are few and far between. Because of the different thermal expansion coefficients of different materials, the dimensions of dissimilar materials will change during the cooling and heating cycles of a tokamak shot. The blanket and shield in particular are complicated structures and might crack due to this expansion effect. They also must withstand the pulsed forces from all of the plasma and coil currents. A truly steady state stellarator avoids these issues. 
  • Stellarator coils are much smaller than tokamak coils. They are twisty, but nowadays computer-controlled machines can easily cope with this. They also have shorter helium cooling paths.

Because stellarator results (especially LHD's) are on a par with tokamak results, and because engineering a stellarator is easier (and hopefully cheaper) than engineering a tokamak, it only makes sense to pause or to stop ITER, and to wait for the results from the Wendelstein 7-X experiment. The costs and timescale of ITER keep increasing, and the scope of the project keeps diminishing. Meanwhile, the world economy is still unhealthy, and funds to support ITER are in short supply. The whole magnetic fusion program could be given a black eye if ITER's woes continue. It is time to face reality. ITER should be stopped or delayed until W7-X results are available. Then the MFE program can properly decide whether the tokamak or the stellarator route is the one to pursue.

 

Comments

Submitted by Glen Wurden on Wed, 04/16/2014 - 15:11

Permalink

Jim,

I really like your article. I tell my non-scientist friends, that the differences between a tokamak and a stellarator are: A large tokamak is EASY to build (and I even mean ITER), but IMPOSSIBLE to operate as designed (due to disruptions). A stellarator is very difficult to build, (even with German engineering), but POSSIBLE to operate as designed.
Furthermore, ITER was a mistake to build before demonstrating a 100% solution to the disruption problem in present tokamaks. Yes, it should be stopped, because it will not be able to perform its stated scientific mission, and is therefore a waste of time and $$$.

Submitted by Glen Wurden on Wed, 04/16/2014 - 15:39

Permalink

Jim,

As you know, there are three problems caused by disruptions in a tokamak.

1). The large thermal quench heat loading on the armor (and the required uniformity to prevent melting), 2). the large electromagnetic forces (which can move structures, or rip apart items inside the vessel), and 3). the resulting runaway electron beam (which at 10 MA in ITER can carry 40-60 MJ of energy), which can basically e-beam weld holes in the armor, right down to the water cooling channels, resulting in water leaks.

Armor tiles in ITER have two conflicting design requirements......be thin and water-cooled to take out the normal heat loads (at 5MW/m^2), and on the other hand, be thick (like ablative Space Shuttle tiles) to survive large transient loading. Unlike in the Large Hadron Collider (LHC), where there is a separate beam dump that its 200 MJ to which the beam can be directed, to protect its superconducting magnet bores, there is no special place in ITER to safely "land" a disrupting plasma.

Now the problem with a Disruption Mitigation System, is that it has to be able to stop all three problems, at the same time, every time. A "solution" for one of the three issues is not a solution if it makes one of the other two problems "worse". Furthermore, if the mitigation system is engaged when it isn't really needed, that has operational consequences too. Finally, for the case of dust/flakes falling into the plasma, in an otherwise "safe" operating regime, it can cause a density-limit/impurity bloom disruption.....there is no "safe" operating regime for a high-current, long-pulse large tokamak.

http://wsx.lanl.gov/Disruptions/Disruption-Risk-poster-Wurden-LAUR-11-1…

Submitted by John Sheffield on Thu, 04/17/2014 - 06:58

Permalink

I agree with many of Jim's views. there is however one big issue for stellarators--particularly modular coil ones--the divertor. The poloidal divertor in a tokamak is axi-symmetric, and geernally speaking there aren't many energetic ions on weird orbits. nevertheless, even in a tokamak, true steady state at high power density has not been demonstrated, and one has to worry that the divertor region may not survive long enough. The situation for a stellarator is worse, even for a torsatron-heliotron, because of the higher level of energetic ions on loss orbits. For a modular device this is even worse because the divertor will not be continuous and there will be edges. The siltuation is ameliorated somewhat by the higher density at which the stellarators can operate.

Submitted by jarome on Thu, 04/17/2014 - 08:09

In reply to by John Sheffield

Permalink

Glen has done a detailed study of the issue of handling disruption power on the wall in ITER, and basically just a few disruptions will put a hole in the vacuum vessel. ITER also will have a huge amount (~10 MA) of runaway electrons (produced by the loop voltage) that will have to be handled in a disruption. There are no wall materials that are good enough to handle a disruption, which probably will not deposit its energy uniformly.

John is right about the issue of particle/power-handling in a running steady-state tokamak or stellarator. It is certainly an area of needed research for both confinement types. But you could design a stellarator to have more than one divertor region per period to increase the area. I disagree about the "weird orbits." The whole idea of the quasi configurations is that you get a third quasi-constant of the motion, which confines the energetic ions better than in a conventional stellarator. That being said, the orbits (which conserve J*) certainly have a larger radial extent than banana orbits in a tokamak.

ITER does not have a self-consistent design, let alone a self-consistent burning operational scenario. It is unclear whether either a tokamak or a stellarator could be an economic power reactor. If the wall problem cannot be solved, perhaps a liquid metal wall will be required (immune to neutron damage). In this case, toroidal configurations cannot be used at all. These are all good reasons to stop ITER and to continue research on materials and alternatives to tokamaks.

Submitted by Glen Wurden on Thu, 04/17/2014 - 13:56

Permalink

Jim,

As you know, there are three problems caused by disruptions in a tokamak.

1). The large thermal quench heat loading on the armor (and the required uniformity to prevent melting), 2). the large electromagnetic forces (which can move structures, or rip apart items inside the vessel), and 3). the resulting runaway electron beam (which at 10 MA in ITER can carry 40-60 MJ of energy (more than the initial 20 MJ due to conversion of some of the poloidal field energy to more runaways as dI/dt occurs), which can basically e-beam weld holes in the armor, right down to the water cooling channels, resulting in water leaks.

Armor tiles in ITER have two conflicting design requirements......be thin and water-cooled to take out the normal heat loads (at 5MW/m^2), and on the other hand, be thick (like ablative Space Shuttle tiles) to survive large transient loading. Unlike in the Large Hadron Collider (LHC), where there is a separate beam dump that its 200 MJ to which the beam can be directed, to protect its superconducting magnet bores, there is no special place in ITER to safely "land" a disrupting plasma.

Now the problem with a Disruption Mitigation System, is that it has to be able to stop all three problems, at the same time, every time. A "solution" for one of the three issues is not a solution if it makes one of the other two problems "worse". Furthermore, if the mitigation system is engaged when it isn't really needed, that has operational consequences too. Finally, for the case of dust/flakes falling into the plasma, in an otherwise "safe" operating regime, it can cause a density-limit/impurity bloom disruption.....there is no "safe" operating regime for a high-current, long-pulse large tokamak.

http://wsx.lanl.gov/Disruptions/Disruption-Risk-poster-Wurden-LAUR-11-1…

Submitted by jarome on Fri, 04/18/2014 - 13:38

Permalink

As you can see from the above, the introduction of large currents, concommitant loop voltage, and runaways introduces the need for major expensive auxiliary systems to:

  • Initiate the currect (central solenoid)
  • Carefully measure the current profile on a few ms timescale
  • Control the current profile (by rf and microwaves, pellets to modify the density profile)
  • Drive the current in "steady state" (neutral beams, rf, microwaves)
  • Handle the power from any disruptions (armor)
  • Try and prevent disruptions (control parameters, use extra "disruption-prevention" coils)
  • Mitigate disruptions
  • Stop ELMs (a type of edge disruption)
  • Handle runaway electron dumps

None of these systems have anything to do with actually making fusion, and in a reactor, they cause a large amount of the plant's power output to be used to run these systems. Plasma current in a reactor is evil.

Stellarators with only small plasma currents caused by increasing plasma pressure, do not have or need the above systems to operate. That is why I say it is easier and cheaper to engineer a stellarator.

Add new comment

Comment

  • No HTML tags allowed.
CAPTCHA This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.